Corner cuts and their polytopes

Irene Müller

Abstract: Corner cut polytopes (or staircase polytopes) were first defined by Shmuel Onn and Bernd Sturmfels in a computational commutative algebra context. They owe their name to the fact that their vertices are in one-to-one correspondence with certain partitions of natural numbers, so called corner cuts.

In this paper, we discuss some structural, nonetheless esthetic aspects of corner cut polytopes. In the 2-dimensional case, we draw a connection between a natural linear order on the vertices and a classical partial order on partitions. Furthermore, we explore the relationship between corner cuts and the face structure of corner cut polytopes.